Surjective polymorphisms of reflexive cycles

TL;DR

This paper proves that all reflexive cycles with girth at least 4 have the property that all their surjective polymorphisms are essentially unary, contributing to the understanding of their algebraic structure.

Contribution

It establishes that reflexive cycles of girth at least 4 are Slupecki, meaning all their surjective polymorphisms are essentially unary, a new result in algebraic graph theory.

Findings

Reflexive cycles of girth ≥ 4 are Slupecki.

Surjective polymorphisms of these cycles are all essentially unary.

The result advances understanding of polymorphism structures in reflexive graphs.

Abstract

A reflexive cycle is any reflexive digraph whose underlying undirected graph is a cycle. Call a relational structure Slupecki if its surjective polymorphisms are all essentially unary. We prove that all reflexive cycles of girth at least 4 have this property.